[aaeamdar]

The double colon ("::") is a namespace operator. For example, one of the namespaces in C++ is the standard namespace, "std". So you could say,

"std::cout" etc

since cout is in the std namespace.

You could also say at the beginning of your program:

"using namespace std;"

This would allow you to implicitly refer to the std namespace.

The dot operator is different. It allows you direct (non-pointer) access to data members of a class. For example, if you had some class Apple, you might have a call such as...

"myApple.color" which could be red, yellow, greeen, etc. I don't fully understand jtdowney's code, since I am not at all familiar with the new interface, but this is the meaning of the dot operator versus double colon.